The population mean is $51,400 and the population standard deviation is $4,000. When the sample size is n = 20, there is a 0.4246 probability of obtaining a sample mean within +/- $500 of the population mean.
a. What is the probability that the sample mean is within $500 of the population mean if a sample of size 40 is used
b. What is the probability that the sample mean is within $500 of the population mean if a sample of size 80 is used